Ok /sci/entists, we all know you can't divide by zero, but

>>8427155
>but WHY exactly can't you divide by zero?

Because you aren't technically dividing.

You can't divide by zero because humans didn't find any logic in that

Maybe dividing by zero would lead to an infinite result ?

>>8427155
https://en.wikipedia.org/wiki/Division_by_zero
s@ge

>>8427159
You can make it infinity if you want. You just have to explain that you're using a different set of numbers.

Mathematicians are always exploring new mathematical constructs, and seeing how useful or interesting/deep they are. It's perfectly valid to define 1/0 as something, and then see where that takes you. You'll probably have to change a few other rules, too though.

But usually it doesn't help us any. For instance, you've all seen the meme puzzles that end up proving 1=2 by dividing by zero. That's not something that people want to be true, so we say that that's an illegal move.

OP, don't make the mistake of thinking there is something inherent in the universe that magically tells us how to divide. Mathematics is a set of rules, that sometimes helps us describe the world around us.

What I'm saying is, you just cant.

Zero was a mistake, prove me wrong.

>>8427155
something shared by nothing is eternal

>>8427155
Since division is just fancy terms for subtracting by a number an x amount of times, you cant divide by zero because you could subtract by zero an infinite amount of times and never get an answer

>>8427155
It's just the logical conclusion of the definition of dividing. If you're not dividing by "something" then you're not doing it.

Kinda like how being an OP means you'r not doing it

>>8427155
If you take division of 100/x, that means that x gets 100. If x=0 then no one gets 100.

Basically this
>>8427226

>>8427155
You can. The answer in infinity. Or, at the very least, it tends towards infinity.

>>8427155
Because it doesn't make any sense. You're literally asking how many slices you'd have to take of something end up with 0 pieces. you can't rearrange something in a way that is less than the starting value. Be aware that math is just the logical system for interpreting the world in our brains. Math, is not real. Math is the name we give to the system we use to interpret reality. it has no bearing on what is actually in the universe. Accurate mathematics is more complicated than we can even comprehend. If you remove time from this bullshit, then you see. Time isn't real, and it's illusion to us is what gets in the way of our mathematics lining up perfectly with the universe. It'd be easier to measure a value in a single instant, but because we're time dependent entities, we need an arbitrarily large amount of moments.

>>8427192
This.

>>8427245
So yeah>>8427244 is right, I'm saying, you'd need to be free of time to do an infinite amount of things. the fact that we have reason do anything at all means we can't divide by zero. it's completing a calculation, which takes time to get from not knowing to knowing. The answer is infinity, cuz that's how many times you'd have to divide something to get nothing, mathematically. but we can't do an infinite amount of things. It's a paradox created from our inability to do everything at once, basically

>>8427192
This is the best answer.

>>8427155
>WHY exactly can't you divide by zero?
But you can

0/0

>>8427155
Am I the only one that gets triggered by this gif? It's should be collapsing exponentially faster as you look further into the picture but it's not.

The answer is nothing. It's divided by zero.

One pizza divided into two parts is two parts of pizza.

One pizza divided into zero parts is zero parts of pizza.

Dividing my zero is literally reducing something to zero, it's like multiplying by zero.

>>8427937
But that's wrong.

1/0 = ∞
2/0 = ∞

1=2

bippity bopity boo

>>8428018
No sir
Brainlet spotted
Terrorists win

There's no element in [math]\mathbb{R}[/math] that you could assign to be the inverse of 0 while satisfying all the axioms of a field.

Each non-zero element already has a unique, non-zero inverse. It also can't be its own inverse since it's trivially provable that for all [math]x \in \mathbb{R}[/math], x * 0 = 0, thus 0 * 0 = 0, thus it's not true that 0 * 0 = 1.

>>8427155
Think of it like this...

The numerator represents pizzas.
The denominator represents friends with which to share the pizza.

If I have 0/14 then I'm with all of my friends but I don't have any pizza to share with them

If I have 14/0 then I have 14 pizzas and no friends

It's not that you can't divide by zero, it's just that if you do, you become OP

>>8427848
0/0 is indeterminate

>>8428026
a=b

a^2=ab

a^2-b^2 = ab-b^2

(a+b)(a-b) = b(a-b)

a+b = b

a+a = a

2a = a

2 = 1

>>8427155
Because something cannot be split into nothing.
Two can be divided into two groups of one.
But, two cannot be divided into zero groups.
Personally, divided by zero should equate to zero, I cannot think of a more reasonable answer.

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>>8428056

>>8427155
You can't divide non-zero numbers by zero because of the following:

x/0 = q
x = q*0
x = 0

The answer is undefined; there is no number q which will multiply by 0 to give non-zero value x. You might as well ask for a number less than 1 and greater than 2, or the third factor of a prime. Dividing by zero is just a very concise way of writing nonsense.

Of course, the above argument doesn't apply if x does equal zero:

0/0 = q
0 = q*0
0 = 0

Perfectly valid. Only problem is, this holds true for any value of q, because anything*0 = 0. Therefore the answer is also undefined. You can't nail down a value for 0/0 like you can for other statements. It's a meaningless statement, x = 0/0 is like saying "x equals something".

>>8427181
So fucking wrong. Zero is God's number.

>>8427155
Zero has no value.

>>8428018
Once you get into evaluating infinite series, you learn that there are different levels of infinity.

n! >> x^n >> x*n as n-> inf

It's an extremely useful abstraction, but it's good to remember that it is a moving target.

>>8428641
And also not so relevant because the infinity yielded by 1/0 and 2/0 would be the same infinity, and thus
1=0*inf
2=0*inf
1=2

>>8428648
disagree, anon.

Neither of those values is infinity, mathematically or otherwise. They are both DNE and NaN, same as log(0). It's not an allowable mathematical operation.

Infinity exists, but it is not a number in the traditional sense.

Infinity = lim a -> 0 of x/a, where x is any nonzero real. Applying this to your example:

infA = lim a -> 0 of 2/a
infB = lim a-> 0 of 1/a

infA = 2(infB)

They are not the same infinity, and the 3rd equation is not true. QED.

>>8427155
By definition, division by x = multiplication by the inverse of x relative to multiplication (i.e. the number y such that y*x =1).
0 has an absorbance property :0*y = 0, for all y.
ergo y*0=1 doesn't have a solution
ergo 0 doesn't have an inverse
ergo you can't divide by 0.

>>8428641
What you showed are not "different levels" of infinity. The sequences with terms n!, x^n (for x > 1), and x*n (for x > 0) each tend toward infinity. It's true that for a given, sufficiently large n, n! > x^n > x*n, but the [math]\infty[/math] we put on the other side of the equal sign when evaluating a limit is not a number. It's a symbol meaning the sequence's terms are arbitrarily large for large enough n. And it's the same symbol with the same meaning for each of these sequences.

The classic example of "some infinities are larger than others" has to do with cardinal numbers. [math]\aleph_0 < \mathfrak{C}[/math].

>>8429710
the point of symmetry has no symmetry

Division is multiplication with the inverse. The inverse is the number you multiply with to get one. Zero has no inverse since everything you mutiply by zero is zero.

>>8427192
This is the best answer.

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Division by zero is undefined. Pic related.

>>8427155
You cannot divide by zero because zero is not a value, it's a place holder. It exists to indicate the lack of something, not the presence of something.

When you write 204, the 2 indicates a value of twice one hundred, the 0 indicates there are no multiples of ten, and the 4 indicates there are four multiples of one.

You're trying to divide by something that indicates nothing.

>>8430016
>zero is not a value, it's a place holder. It exists to indicate the lack of something, not the presence of something.
This is so wrong it hurts.

>>8429804
/thread
R we done yet

>>8429732

Ah, but those limits are all different levels of infinity. Predicting convergence for infinite series is often impossible without this being the case.

Infinity is an abstract, and not an exact value. It's a stand in for "some number too fucking big to write down if you spent the rest of your life writing". It exists, but it's value is undefined.

Unlike x/0 which is a nonsense statement. You can't subdivide something zero times.

>>8429739
This is so deep and mystical and bullshit and unrelated...

>>8427155
There are 4 cookies divided among 2 people. How many cookies does each person have? 2.

There are 0 cookies divided among 2 people. How many cookies does each person have? 0.

There are 4 cookies divided among 0 people. How many cookies does each person have? Undefined.

>>8428056
>2a = a
>2 = 1
and
>(a+b)(a-b) = b(a-b)
>a+b = b
>nobody answered this yet
you divided by zero but then didn't write out ∞=∞

>>8428056
assume a=0

Now you whole bullshit falls apart.

>>8427155
Dividing by nothing means you aren't actually dividing.

>>8430682
no, it falls apart because a = b, so (a-b) = 0 and at one point the equation was divided by (a-b), that is divided by zero

>>8427155
BECAUSE IF YOU HAVE SIX COOKIES AND DIVIDE THEM AMONG ZERO FRIEDNS, HOW MANY COOKIES DOES EACH FRIEND GET?

$1/0=x$ implies $1=0$.
Now if you do your computations somewhere where $1=0$, then it's totally fine to divide by zero there, but in the real numbers (with addition and multiplication) field, one is hella different of zero.

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>>8427155
[eqn]\frac{x}{0}=0[/eqn]

For all real [math]x[/math]. Prove me wrong

>>8428051
I'm not using ZFC

>>8427155
math is a construct used to quantify the world we see, ain't no shiznit bout the rules we make.
zero is a place holder with no value, a convenience for linear scale. stupid for logarithmic scale.

try getting laid

>>8432794
I'll do the classic proof by contradiction:

suppose that for all real x, x/0 = 0
Hence, 1/0 =0
2/0 = 0
1/0 = 2/0
Multiply both sides by 0...
1=2 Contradiction!

>>8427155
God most of the answers in this thread are fucking retarded. There is nothing inherently bad mathematically with dividing by zero, it's just that it doesn't work in the system of numbers that most people are familiar with. If you want to divide by zero in a mathematically meaningful way you can, it's called the projective line. It is a very useful and mathematically interesting construction.

You can't in the usual field of real numbers because of the following property of 0: 0*x=0, for all x (so there is no expression for 1/0 in the real numbers)

But you can get around this issue by working in a slightly different mathematical structure. Essentially you add in an infinity element into your real numbers and extend arithmetic in the following way.

1/0 = infinity, 1/infinity = 0, x* infinity = infinity (for all x except 0) and x + infinity = infinity ( for all x)

What you get is the real projective line https://en.wikipedia.org/wiki/Projective_space

>>8427192
this

>>8428056
>(a-b)
>a=b
>therefore (a-b)=0
>(a-b)/(a-b) = 0/0

smoke and mirrors

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>>8433224
>1=2
>contradiction

nice spook